Romeo and Juliet is certainly full of allusions to mythological gods. While there are far too many to discuss all of them here, below are listed two that can be seen in the very first scene alone to help get you started.
One mythological god frequently alluded to in Romeo and Juliet is Cupid, and this allusion can first be found in Act 1, Scene 1. Cupid is the Roman god of erotic love, passion, and desire. He's the son of Venus, the goddess of love. We first see him being alluded to in Romeo's lines, "Alas that love, whose view is muffled still, / Should without eyes see pathways to his will!" (I.i.169-70). We know that this is a clear allusion to Cupid because Cupid is often depicted as being a blindfolded youth. His blindfold symbolizes that erotic love is arbitrary, that there really often are no concrete reasons for why we erotically fall in love with the people we do. Plus, Cupid is said to make people fall in love by shooting his flaming arrows at them. Therefore, Romeo is lamenting how frustrating it is that personified blind love should still be able to make people do his bidding by arbitrarily making people fall in love, which is a clear allusion to Cupid.
A second mythological god frequently alluded to is Diane, which can also be found in the very first scene. Diane is the Roman goddess of the moon, hunting, and child birthing. Ironically, even though she is the goddess of child birthing, she is actually a sworn virgin herself. Romeo alludes to Diane when he draws an analogy between the goddess and Rosaline, stating that like Diane, Rosaline has taken a vow of chastity, as we see in his lines:
She hath Dian's wit,
And, in strong proof of chastity well arm'd,
From Love's weak childish bow she lives unharm'd. (I.i.211-13)
Since in these lines he refers to the name "Dian" plus to chastity, we see that these lines serve as an allusion to the goddess Diane.